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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 172v, page id 00068195:0344
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Jureni supra aequationem ali ordinatae demissae ex curva eonica, ad  ex
 rectam ex vertice intsa curvam ulcuque ductams, nempe abscissa cjus rectae, posita 
ert applicata ad angulos rectos:
in Daita sectione, qinvenie valorem rectae YX ex ob curva
Abscissam ex axe A applicatae angulo dato, ita
cum
scilice ut ratio rectarum YB ad XB, sit data C ad q.
Sit AX  y. ex _7(+) ZB (e) datur ZB, N
erit enim YB e P2ya  ea + La y + a c+(+ 2
At eadem YB datur ex e, data, erit enim YB C.
Ergo erit X  2ya (F) rea ec.
ordinandoque erito
Eritque e +n 1 ya + a yt rri
poranus pu , Va res1 y
F
ea
enXB
uitin e
n
Nimis prolixus fit
calculus.
i
9
In cuculo ex recta AX, quaentuo
ipsa X+ dato angulo
YXB seu 2B r1 4
at AX 4y. XB, jC.
2ax (F) 2ac a X 
Cum detur YH ad YB dabitur et
X4 YX
YB nempe ergo et BC
datur pono et X XE  a - X. ergo et EF
dato datur FY juncteq FY et
FX, dant YX, quaesilam, 1d
re apse excquamur:
AX A X. YBB E XEp, a- X
+B
ex L YeM Ergo XBBC.
Ergo YB  ec o3 Y
Ergo YX res
L 1deC+ e
YB H. 4 Ergo
AYC -XC4
XC B SCA  Ergo Fx 9a -X4 X que quet ac = XC
En 
set qu Data FE, datur jam FY estqu a a  Aep. 8. l N - aY O + er o -rat An + 8no 4n Bah+ 2n B k - anb  g
Ergo YX,  hoc est FY +
+
VX, 1) S a a - 2aX +
eet qu
Substituatur y habebimus YXN
Sc+qu
+4
 ent Lee
 + 4a - Xq
Si loco a - x,
X ad g+ C+ qu, C
pro a ponatur b ut in alto Aqualio re maned = + 4
et pro 2 ponatur y
4
et )a  () ZC +n ri2ya
) +
Unde fiet XB7 Eya ( ran +a 44y rn
et FE p
ac
+a
1
+ ay + 2a y 
Sc+
quadrando, et ordimando tiet + 2a y +2a 1) = b  29A
P A q erqu
4
et FX
er cum detur BC,3